# A Fuzzy Edge Detector Driven Telegraph Total Variation Model For Image Despeckling

## TL;DR

This paper introduces a novel despeckling method combining telegraph total variation and fuzzy set theory, effectively reducing speckle noise while preserving image details in natural and SAR images.

## Contribution

It proposes a new fuzzy edge detector driven telegraph total variation model for speckle noise suppression, incorporating IFD and establishing mathematical properties like existence and uniqueness.

## Key findings

- Better noise suppression compared to existing methods
- Enhanced edge and detail preservation in despeckling
- Effective on both natural and SAR images

## Abstract

Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for speckle noise suppression. The intuitionistic fuzzy divergence (IFD) function has been used to distinguish between edges and noise. To the best of the author's knowledge, most of the studies on multiplicative speckle noise removal process focus on only diffusion-based filters, and little attention has been paid to the study of fuzzy set theory. The proposed approach enjoy the benefits of both telegraph total variation equation and fuzzy edge detector, which is not only robust to noise but also preserves image structural details. Moreover, we establish the existence and uniqueness of a weak solution of the regularized version of the proposed model using Schauder fixed point theorem. With the proposed model, despeckling is carried out on natural and Synthetic Aperture Radar (SAR) images. The experimental results of the proposed model are reported, which found better in terms of noise suppression and detail/edge preservation, with respect to the existing approaches.